Physics 1B! Electricity & Magnetism Frank Wuerthwein (Prof) Edward Ronan (TA) UCSD Quiz 1 • Quiz 1A and it’s answer key is online at course web site. • http://hepuser.ucsd.edu/twiki2/bin/view/ UCSDTier2/Physics1BWinter2012 • Expect to have grades up on web site by Friday evening this week. Outline of today • Continue Chapter 20. • Equipotentials • Parallel plates • Capacitance Equipotentials • An equipotential surface is a surface on which all points are the same potential. • It takes no work to move a particle along an equipotential surface or line (assume speed is constant). • The electric field at every point on an equipotential surface is perpendicular to the surface. • Equipotential surfaces are normally thought of as being imaginary; but they may correspond to real surfaces (like the surface of a conductor). Equipotentials • Let’s construct an equipotential surface for a lone negative charge. -10V " ! First, draw the field lines for -20V the charge. " ! If I move 1m away would -30V it matter if it was up or – down or left or right if I were to calculate potential? " ! No, so our equipotential surface would be a sphere. " ! Also, since V goes as (1/r), the spacing would increase between equipotential surfaces. Equipotentials •! For a lone positive charge, the equipotential surfaces are all spheres centered on the charge. •! We represent these spheres with equipotential lines. " ! Equipotential lines are shown in blue, electric field lines are shown in red. " ! Note that the field lines are perpendicular to the equipotential lines at every crossing. Equipotentials •! As you increase the number of charges in the distribution the equipotential lines get more complicated. •! Take the electric dipole composed of a positive and a negative charge. Parallel Plates •! If we had a very large plane of positive charge, what would the electric + + + + + + + + field look like? •! The electric field would be uniform in both directions away from the positive plate. " ! A positive charge on either side of the plate (top or bottom) would be repelled. Parallel Plates " ! What would be different if the plate were negative (but had the same magnitude of charge)? – – – – – – – – " ! The electric field would flip direction (in toward the negative plate), but still have the same magnitude. " ! A positive charge on either side of the plate (top or bottom) would be attracted. Parallel Plates + + + + + + + + •! What would now happen if I place the plates close together and parallel to each other? •! The field would be twice as strong in between the – – – – – – – – plates, but would essentially disappear " ! Equipotential lines are outside of the plates. evenly spaced! " ! What would the equipotential lines look like between the plates? Parallel Plates •! If I were to place a positive charge, q, in between the plates and then release it, what would happen? " ! The positive charge would move away from the positive plate (high PE, high V) toward the negative plate (low PE, low V). " ! The work done by the electric field would be: ! ! W = Felec " #x ! ! W = qE " #x = $#PE ! ! Parallel Plates • If we were to then turn to electric potential, we can say that: " ! This is true for a uniform electric field. " ! But, general, you can always say that: " ! These equations just reiterate that if you move with the electric field, your electric potential will decrease. Parallel Plates •! We put opposite charges on two parallel plates and we create an electric field in between the plates. •! This is essentially storing energy between these plates by creating an electric field between them. •! We call such a device: Capacitor •! Next we will talk about how to characterize the electrical properties of such a device. Capacitors •! Capacitance, C, is a measure of how much charge can be stored for a capacitor with a given electric potential difference. " ! Where Q is the amount of charge on each plate (+Q on one, –Q on the other). " ! Capacitance is measured in Farads. " ! [Farad] = [Coulomb]/[Volt] " ! A Farad is a very large unit. Most things that you see are measured in μF or nF. Capacitors •! Inside a parallel-plate capacitor, the capacitance is: " ! where A is the area of one of the plates and d is the separation distance between the plates. " ! When you connect a battery up to a capacitor, charge is pulled from one plate and transferred to the other plate. Capacitors " ! The transfer of charge will stop when the potential drop across the capacitor equals the potential difference of the battery. " ! Capacitance is a physical fact of the capacitor, the only way to change it is to change the geometry of the capacitor. " ! Thus, to increase capacitance, increase A or decrease d or some other physical change to the capacitor. Concept Question •! You connect a capacitor to a 1.5V battery and you get a certain amount of charge Q on each plate. Which of the following happens if you replace the 1.5V battery with a 3.0V battery. " ! A) The capacitance, C, of the capacitor doubles. " ! B) The capacitance, C, of the capacitor halves. " ! C) The charge, Q, on each plate doubles. " ! D) The charge, Q, on each plate halves. " ! E) Neither C nor Q changes. •! ExampleCapacitance •! A parallel-plate capacitor is connected to a 3V battery. The capacitor plates are 20m2 and are separated by a distance of 1.0mm. What is the amount of charge that can be stored on a plate? •! Answer •! Usually no coordinate system needs to be defined for a capacitor (unless a charge moves in between the plates). •! Start with the equation for a parallel-plate capacitor. Capacitance " Answer " ! Start with: " ! Next, turn to the definition of capacitance: Capacitors •! Capacitors are usually used in circuits. •! A circuit is a collection of objects usually containing a source of electrical energy (like a battery). •! This energy source is connected to elements (like capacitors) that convert the electrical energy to other forms. •! We usually create a circuit diagram to represent all of the elements at work in the real circuit. Circuits •! For example, let’s say that we had two capacitors connected in parallel to a battery. •! In the circuit diagram we would represent a capacitor with a parallel line symbol: || •! Also, in the circuit diagram we would represent a battery with a short line and a long line: i| •! The short line representing the negative terminal and the long line representing the positive terminal. Capacitors •! The previous real circuit can then be drawn as a circuit diagram as follows: " ! In this circuit, both capacitors would have the same potential difference as the battery. " ! ΔVbat = ΔV1 = ΔV2 •! Plus, we can say that the charges on either plate are equal to the total that passes through the battery. •! QTo t = Q1 + Q2 Capacitors •! We can essentially replace the two capacitors in parallel with one equivalent capacitor (this may make our life easier). " ! The equivalent capacitor must have exactly the same external effect on the circuit as the original capacitors. " ! The battery sees QTo t passing through it and believes that the one equivalent capacitor has a potential difference of ΔV. For Next Time (FNT) •!Prepare for the Quiz on Friday •!Continue homework for Chapter 20 •!Keep reading Chapter 20 .